Mathematical Programming

, Volume 107, Issue 1–2, pp 5–36 | Cite as

Tractable Approximations to Robust Conic Optimization Problems

  • Dimitris BertsimasEmail author
  • Melvyn Sim


In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general conic optimization problems that (a) preserves the computational tractability of the nominal problem; specifically the robust conic optimization problem retains its original structure, i.e., robust LPs remain LPs, robust SOCPs remain SOCPs and robust SDPs remain SDPs, and (b) allows us to provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.


Robust Optimization Conic Optimization Stochastic Optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Boeing Professor of Operations Research, Sloan School of Management and Operations Research CenterMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.NUS Business SchoolNational University of SingaporeSingapore

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